An Algorithm to Check Whether a Basis of a Parametric Polynomial System is a Comprehensive Gröbner Basis and the Associated Completion Algorithm

Kapur, Deepak; Yang, Yiming

doi:10.1145/2755996.2756676

Cited by 1 publication

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“…Recall that every polynomial in the CGB generated by the KSW algorithm is faithful since every polynomial in the GB of every segment of its CGS is faithful. In a related paper [7], we have proposed a Buchberger like completion algorithm for computing a minimal CGB directly from a basis of a parametric ideal.…”

Section: Introductionmentioning

confidence: 99%

An efficient algorithm for computing a comprehensive Gröbner system of a parametric polynomial system

Kapur

Sun

Wang

2013

Journal of Symbolic Computation

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An algorithm to generate a minimal comprehensive Gröbner basis of a parametric polynomial system from an arbitrary faithful comprehensive Gröbner system is presented. A basis of a parametric polynomial ideal is a comprehensive Gröbner basis if and only if for every specialization of parameters in a given field, the specialization of the basis is a Gröbner basis of the associated specialized polynomial ideal. The key idea used in ensuring minimality is that of a polynomial being essential with respect to a comprehensive Gröbner basis. The essentiality check is performed by determining whether a polynomial can be covered for various specializations by other polynomials in the associated branches in a comprehensive Gröbner system. The algorithm has been implemented and successfully tried on many examples from the literature. Keywordscomprehensive Gröbner basis, minimal comprehensive Gröbner basis, parametric polynomial system, specialization of polynomial systems, essentiality.

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Section: Introductionmentioning

confidence: 99%

An efficient algorithm for computing a comprehensive Gröbner system of a parametric polynomial system

Kapur

Sun

Wang

2013

Journal of Symbolic Computation

Self Cite

View full text Add to dashboard Cite

show abstract

An Algorithm to Check Whether a Basis of a Parametric Polynomial System is a Comprehensive Gröbner Basis and the Associated Completion Algorithm

Abstract: Given a basis of a parametric polynomial ideal, an algorithm is proposed to test whether it is a comprehensive Gröbner basis or not.

Cited by 1 publication

References 18 publications

An efficient algorithm for computing a comprehensive Gröbner system of a parametric polynomial system

An efficient algorithm for computing a comprehensive Gröbner system of a parametric polynomial system

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